Sea Wall – which was written especially for Scott and first performed at the Bush Theatre in 2008 – is a one-man play about family, fear and the things that can't be undone.
The Paines Plough production forms part of the Old Vic's 200th-anniversary celebrations when it runs at the theatre from 18 to 30 June.
Sherlock star Scott was most recently on stage in Robert Icke's production of Hamlet at the Almeida and in the West End. His previous theatre credits include The Dazzle, Birdland, Design For Living and Cock.
Stephens is best known for his multi-award-winning stage adaptation of Mark Haddon's novel The Curious Incident of the Dog in the Night-Time. His other plays include Bluebird, Port, Punk Rock and Heisenberg.